Question

Definition of parallel axis therom and perpendicular axis therom

Answer 1

The states that the "moment of inertia of any object about an axis through its center of mass is the minimum moment of inertia for an axis in that direction in space," according to HyperPhysics. It is also known as Steiner's theorem.parallel axis theorem
It can be used as a shortcut to find moments of inertia for objects when the axis of rotation is somewhere other than the center of mass of the object. If the inertia is known for objects when going through the center of mass, the new value of I can be found for any axis that is parallel to the center of mass axis and displaced by some distance from the center of mass, d.

For a planar object, the moment of inertia about an axis to the plane is the sum of the moments of inertia of two perpendicular axes through the same point in the plane of the object. The utility of this theorem goes beyond that of calculating moments of strictly planar objects. It is a valuable tool in the building up of the moments of inertia of three-dimensional objects such as cylinders by breaking them up into planar disks and summing the moments of inertia of the composite disks perpendicular